Year: 2025
Type: article
Abstract: We introduce a higher uniformity analogue of graphic zonotopes and permutohedra. Specifically, given a ‐uniform hypergraph , we define its hypergraphic zonotope , and when is the complete ‐uniform hypergraph , we call its hypergraphic zonotope the acyclohedron . We express the volume of as a homologically weighted count of the spanning ‐dimensional hypertrees of , which is closely related to Kalai's generalization of Cayley's theorem in the case when (but which, curiously, is not the same). We also relate the vertices of hypergraphic zonotopes to a notion of acyclic orientations previously studied by Linial and Morgenstern for complete hypergraphs.
DOI: 10.1112/blms.70221
Authors: Cosmin Pohoata, Daniel G. Zhu
Institutions: Emory University, Princeton University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4415618764